One conventional device for mapping the topography of an eye is referred to as a "Placido." As shown in respective front and side views in FIGS. 1A and 1B, a Placido 10 typically includes a series of illuminated concentric rings 12. In order to map the topography of the eye 14, the Placido 10 is positioned in alignment with the eye 14 so the rings 12 reflect off the tear film on the cornea 16 and travel through an aperture 18 in the Placido 10 to a camera 20 that records images of the reflected rings 12 (to clarify the illustration, FIG. 1B depicts the reflection of only some of the rings 12 off the cornea 16). Analysis of these recorded images, including analysis of the shape and position of the reflected rings 12, provides an approximation of the slope of the eye 14 at the points on the eye 14 where the rings 12 were reflected. A surface suitable for display can then be mathematically "fit" to the approximate slopes at these points using various techniques well-known to those of skill in the art.
As shown in more detail in a top view in FIG. 2, analysis of the recorded image of a point P on one of the rings on the Placido 10 reflecting off the cornea 16 of the eye 14, passing through the aperture 18 in the Placido 10, and striking a Charge Coupled Device (CCD) 30 in the camera 20 at point I proceeds as hereinafter described. A central portion 32 of the cornea 16, enclosed by the innermost ring of the Placido 10 reflecting off the cornea 16, is approximated by fitting the central portion 32 with a partial sphere having a radius of curvature R.sub.0. Also, the apex point E.sub.0 of the cornea 16 is assumed to have a Normal 36 (i.e., an orthogonal vector) that is coincident with the optical axis 38 of the camera 20. The point E.sub.1 on the cornea 16 where point P reflects off the cornea 16 is then approximated by assuming a constant curvature between ring edges on the cornea 16.
Using this "constant curvature" technique, a radius of curvature R.sub.1 and coordinates (x.sub.1, z.sub.1) are determined iteratively for point E.sub.1 such that a Normal 40 at point E.sub.1 has equivalent angles of incidence .alpha. and reflection .theta.. The surface of the cornea 16 between points E.sub.0 and E.sub.1 is then assumed to be a partial sphere having radius of curvature R.sub.1. This process is repeated until (x,z) coordinates and a Normal are approximated for all points of reflection of the rings of the Placido 10 off the cornea 16. Knowledge of the Normal of each of these points then permits the calculation of a slope at each point and, in turn, the fitting of a surface to the points as previously described. More information regarding the general operation of Placidos may be found in U.S. Pat. No. 3,797,921 to Kilmer et al.
Because the described Placido utilizes certain assumptions about the eye being measured that are not necessarily true, namely, that the curvature of the cornea between successive Placido rings is constant, and that the surface normal at the apex of the cornea is coincident with the focal axis of the camera, the Placido is not as accurate as is desirable. Consequently, other techniques have been devised for more accurately mapping the topography of an eye.
One such technique, referred to as "ORBSCANI," was introduced by the Assignee of the present invention, Orbtek, Inc. of Salt Lake City, Utah, and is disclosed and claimed in U.S. Pat. Nos. 5,512,965 and 5,512,966 to Snook. As shown in a top view in FIG. 3 herein, in this technique, a first slit beam 50 of light is stepped from right to left across an eye 52 that is to be mapped, and a second slit beam of light (not shown) then steps from left to right across the eye 52. When the first slit beam 50 reaches the anterior surface 54 of the cornea 56 of the eye 52, it splits into two components: a specular reflection 58 from the anterior surface 54 of the cornea 56, and a refracted beam 60 that penetrates the cornea 56 and is refracted (i.e., bent), in accordance with Snell's Law, by the index of refraction between air and the cornea 56. The specular reflection 58 serves no purpose in this technique.
The refracted beam 60 is scattered within the cornea 56 by a mechanism known as diffuse scattering. Reflections 62 from the intersection point C.sub.ant between the diffusely scattered refracted beam 60 and the anterior surface 54 of the cornea 56, and reflections 64 from the intersection point C.sub.post between the diffusely scattered refracted beam 60 and the posterior surface 66 of the cornea 56, then travel through the focal point of a lens 68 to impinge on a CCD 70 of a camera 72 at respective points L.sub.ant and L.sub.post. Because the relative positions of the light source (not shown) for the first slit beam 50, the eye 52, the lens 68, and the CCD 70 are known, the reflections 62 impinging on the CCD 70 at known point L.sub.ant allow calculation of the space coordinates (x.sub.ant,Y.sub.ant, Z.sub.ant) of the point C.sub.ant. Also, the reflections 64 impinging on the CCD 70 at known point L.sub.post, as well as knowledge of the index of refraction between air and the cornea 56, allow calculation of the space coordinates (x.sub.post,y.sub.post, z.sub.post) of the point C.sub.post. A similar diffuse reflection 74 from the lens 76 of the eye 52, and from the iris 78 of the eye 52 (diffuse reflection not shown from the iris 78), along with knowledge of the index of refraction between the cornea 56 and the anterior chamber 83 of the eye 52, allow calculation of the space coordinates (x, y, z) of points along the respective anterior surfaces 80 and 82 of the lens 76 and the iris 78. Of course, the second slit beam works in the same manner to measure space coordinates (x, y, z) as the first slit beam 50.
By stepping a pair of slit beams across the eye 52 from left to right and from right to left, this technique allows the direct measurement of space coordinates (x, y, z) for thousands of points on the anterior 54 and posterior 66 surfaces of the cornea 56, and on the anterior surfaces 80 and 82 of the lens 76 and the iris 78. Surfaces suitable for viewing can then be mathematically fit to these known points as previously described. Since no assumptions are made regarding the shape of the cornea 56, lens 76, or iris 78, the technique more accurately portrays the surfaces of these parts of the eye 52.
Unfortunately, inaccuracies exist in this technique as well. In particular, limitations in the density of pixels on the CCD 70, and errors in the relative positions of the first slit beam 50, the eye 52, the lens 68, and the camera 72, limit the accuracy of the measurements using this technique typically to about .+-.2 .mu.m (micrometers or "microns").
Therefore, there is a need in the art for an improved device and method for mapping the topology of an eye.